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IMC
2011 IMC
3
IMC 2011 Day 2, Problem 3
IMC 2011 Day 2, Problem 3
Source:
August 1, 2011
logarithms
limit
IMC
college contests
Problem Statement
Calculate
∑
n
=
1
∞
ln
(
1
+
1
n
)
ln
(
1
+
1
2
n
)
ln
(
1
+
1
2
n
+
1
)
\displaystyle \sum_{n=1}^\infty \ln \left(1+\frac{1}{n}\right) \ln\left( 1+\frac{1}{2n}\right)\ln\left( 1+\frac{1}{2n+1}\right)
n
=
1
∑
∞
ln
(
1
+
n
1
)
ln
(
1
+
2
n
1
)
ln
(
1
+
2
n
+
1
1
)
.
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